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Recent dramatic acceleration, thinning and retreat of tidewater outlet glaciers in Greenland raises concern regarding their contribution to future sea-level rise. These dynamic changes seem to be parallel to oceanic and climatic warming but the linking mechanisms and forcings are poorly understood and, furthermore, large-scale ice sheet models are currently unable to realistically simulate such changes which provides a major limitation in our ability to predict dynamic mass losses. In this paper we apply a specifically designed numerical flowband model to Jakobshavn Isbrae (JIB), a major marine outlet glacier of the Greenland ice sheet, and we explore and discuss the basic concepts and emerging issues in our understanding and modelling ability of the dynamics of tidewater outlet glaciers. The modelling demonstrates that enhanced ocean melt is able to trigger the observed dynamic changes of JIB but it heavily relies on the feedback between calving and terminus retreat and therefore the loss of buttressing. Through the same feedback, other forcings such as reduced winter sea-ice duration can produce similar rapid retreat. This highlights the need for a robust representation of the calving process and for improvements in the understanding and implementation of forcings at the marine boundary in predictive ice sheet models. Furthermore, the modelling uncovers high sensitivity and rapid adjustment of marine outlet glaciers to perturbations at their marine boundary implying that care should be taken in interpreting or extrapolating such rapid dynamic changes as recently observed in Greenland

Thomas Zwinger was supported by the Nordic Center of Excellence eSTICC (eScience Tools for Investigating Climate Change in Northern High Latitudes) funded by Nordforsk (grant 57001). Acquisition of the TerraSAR-X imagery was funded by the ConocoPhillips Northern Area Program, via the CRIOS project (Calving Rates and Impact on Sea Level). The lead author received an Arctic Field Grant from the Svalbard Science Forum to acquire radar lines for the basal topography in 2014. In this paper, we study the effects of basal friction, sub-aqueous undercutting and glacier geometry on the calving process by combining six different models in an offline-coupled workflow: a continuum–mechanical ice flow model (Elmer/Ice), a climatic mass balance model, a simple subglacial hydrology model, a plume model, an undercutting model and a discrete particle model to investigate fracture dynamics (Helsinki Discrete Element Model, HiDEM). We demonstrate the feasibility of reproducing the observed calving retreat at the front of Kronebreen, a tidewater glacier in Svalbard, during a melt season by using the output from the first five models as input to HiDEM. Basal sliding and glacier motion are addressed using Elmer/Ice, while calving is modelled by HiDEM. A hydrology model calculates subglacial drainage paths and indicates two main outlets with different discharges. Depending on the discharge, the plume model computes frontal melt rates, which are iteratively projected to the actual front of the glacier at subglacial discharge locations. This produces undercutting of different sizes, as melt is concentrated close to the surface for high discharge and is more diffuse for low discharge. By testing different configurations, we show that undercutting plays a key role in glacier retreat and is necessary to reproduce observed retreat in the vicinity of the discharge locations during the melting season. Calving rates are also influenced by basal friction, through its effects on near-terminus strain rates and ice velocity. Publisher PDF

This work was funded by the ConocoPhillips Northern Area Program (CRIOS: Calving Rates and Impact on Sea Level) and the Nordic Research Council (SVALI: Stability and Variation of Arctic Land Ice and eSTICC: eScience Tools for Investigating Climate Change in northern high latitudes). The simple calving laws currently used in ice sheet models do not adequately reflect the complexity and diversity of calving processes. To be effective, calving laws must be grounded in a sound understanding of how calving actually works. Here, we develop a new strategy for formulating calving laws, using a) the Helsinki Discrete Element Model (HiDEM) to explicitly model fracture and calving processes, and b) the continuum model Elmer/Ice to identify critical stress states associated with HiDEM calving events. A range of observed calving processes emerges spontaneously from HiDEM in response to variations in ice-front buoyancy and the size of subaqueous undercuts. Calving driven by buoyancy and melt undercutting is under-predicted by existing calving laws, but we show that the location and magnitude of HiDEM calving events can be predicted in Elmer/Ice from characteristic stress patterns. Our results open the way to developing calving laws that properly reflect the diversity of calving processes, and provide a framework for a unified theory of the calving process continuum. Publisher PDF

We present results from numerical ice-flow models that include calving criteria based on penetration of surface and basal crevasses, which in turn is a function of longitudinal strain rates near the glacier front. The position of the calving front is defined as the point where either (1) surface crevasses reach the waterline (Model CDw), or (2) surface and basal crevasses penetrate the full thickness of the glacier (Model CD). For comparison with previous studies, results are also presented for a height-above-buoyancy calving model. Qualitatively, both Models CDw and CD produce similar behaviour. Unlike previous models for calving, the new calving criteria are applicable to both grounded termini and floating ice shelves and tongues. The numerical ice-flow model is applied to an idealized geometry characteristic of marine outlet glaciers. Results indicate that grounding-line dynamics are less sensitive to basal topography than previously suggested. Stable grounding-line positions can be obtained even on a reverse bed slope with or without floating termini. The proposed calving criteria also allow calving losses to be linked to surface melt and therefore climate. In contrast to previous studies in which calving rate or position of the terminus is linked to local water depth, the new calving criterion is able to produce seasonal cycles of retreat and advance as observed for Greenland marine outlet glaciers. The contrasting dynamical behaviour and stability found for different calving models implies that a realistic parametrization for the process of calving is crucial for any predictions of marine outlet glacier change.

More than half of the annual mass transfer from whole cryosphere to the world's oceans occurs through calving. Uncertainties in predicting future sea level are partly caused by a lack of knowledge of the behaviour of calving glaciers. A better understanding of the factors that control the response of calving glaciers to climate change is needed to interpret the past or predict the future behaviour of these glaciers in a warmer climate. Over the past years, interest in the response of calving glaciers to climate change has increased considarably. Many bservational and modelling studies have been carried out to investigate the dynamics of the calving process and the associated response of the glacier terminus. It has been suggested that calving glaciers are inherently unstable showing a periodic advance and retreat that may be nearly independent of climate. The cycle of slow advance and rapid retreat of calving glaciers is mainly a function of fjord geometry, water depth at the glacier terminus, and sedimentation at the glacier front. Some other studies show that climate acts as a first-order control on the advance/retreat. Hence, the diverse behaviour of calving glaciers is a result of both internal dynamics and climate. In this thesis the dynamics of tidewater glaciers (temperate grounded calving glaciers) and the involved processes such as iceberg calving, basal sliding, and proglacial moraine bank are investigated. A numerical ice-flow model is developed, which simulates the rapid retreat and slow advance of tidewater glaciers very well. To construct a time-evolving numerical model that simulates the behaviour of calving glaciers, it is necessary to formulate realistic calving boundary conditions. Empirical studies provide two different calving schemes, the flotation and the water-depth model. We introduce two numerical ice-flow models using the water-depth and the flotation scheme. The results show that any model in which the loss of ice at the glacier front increases with water depth shows qualitatively the same behaviour when a submarine undulation is present in the basal topography. These models are applied to Breidamerkurjokull, a large tidewater glacier in Iceland. The results indicate that the flotation model is not capable of producing the observed glacier retreat into deep water very well, whereas the water-depth model reproduces a glacier evolution identical to observation.